You will need to file a part-year return for NY. TX has no state income tax, so you will not file a state return for the time that you lived and worked in TX.
https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year
https://ttlc.intuit.com/questions/2895983-how-do-i-allocate-split-income-for-a-part-year-state-retur...
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